Based on the Wave Energy Capture Spectrum (ECS) theory, the characteristics of the ECS of a cylindrical heaving buoy WEC with consideration of linear PTO damping are studied in this paper. A 3D numerical wave tank (NWT) based on the RANS equations and the two-phase VOF model was established using the CFD software Flow-3D and validated by the corresponding experimental data. The ECSs of the heaving buoy WEC with different settings were calculated by the energy capture fluctuation signal, which was based on the incident wave elevation and the power output of the heaving buoy. The procedures of ECS solution using numerical method were proposed, and the effects of irregular wave, linear PTO damping, and relative draught on the ECS of the heaving buoy were studied, respectively. The results showed that the average period of incident wave is the key control factor of the peak frequency of the ECS. Compared to linear PTO damping, the relatively draught has little influence on the peak frequency of ECS. With the evaluation of the ECS method, the cylindrical heaving buoy WEC shows good adaptability to variable wave conditions and could be further improved by adjusting its ECS.